Continuity mistake: The knife-thrower attempts to use a welder to temporarily blind Bond - we can see in that shot that it's an acetylene torch. However, in earlier shots when the welder is being used (off-camera), the sound is that of an arc welder.
Plot hole: When Bond wakes up in the monsoon palace, his watch is still beeping with the activated tracking mode. Wouldn't somebody have noticed the constant beeping while he was brought there? The tracker is shown to have a range of several hundred meters, so it would certainly have been in range of the transmitter at least part of the time while Gobinda dragged him back to Kamal's palace.
Revealing mistake: When Grischka pins Bond to the cabin door with his knives, he takes out a knife and attempts to kill Bond for killing his twin brother. Bond then opens the cabin door and then kills Grischka by opening the cabin door and throwing a knife into his stomach. If you watch carefully, you can see the cabin door begin to open before Bond pulls the cabin handle down.
Continuity mistake: During the pre-credits sequence, Bond pulls the ripcords on the parachutes of the two guards who are in the truck with him and the guard on the right is holding a rifle in his right hand, but when he is flying in the air in the next shot, the rifle has gone.
Continuity mistake: When Bond and M are driving through Berlin, in the outside shots, their car is a Mercedes-Benz Type W123 standard wheelbase sedan. In the take when the driver is talking, he's driving that vehicle. When the camera switches to Bond and M in the back seat, it's a long-wheelbase V123 Pullman sedan, evidence being the large pop out rear quarter windows and M leaning forward to open his door. (01:17:57)
Continuity mistake: When Bond is fighting Gobinda on the roof of the train carriage, Grischka appears and you can see from behind he puts his left hand on the roof, but when the camera angle changes in the next shot, Grischka now has his right hand on the roof.
Factual error: When Bond is fighting with Glenda on the wagon roof, shortly before passing a tunnel, which is supposed to be already in West Germany, a communist slogan is visible on the tunnel entry, stating 'Our contribution to a positive balance: daily fulfillment of the plan'. Not something that would be on the west side.
Continuity mistake: Bond arrives in West Berlin to travel to Karl-Marx-Stadt. The Mercedes stops just before Checkpoint Charlie and the other guy gets out of the car. One can see the license plate - which appears to be genuine German (DIN font and spacing etc). When the "same" car later arrives at the Circus the plates are obviously props. The font is off and the plates are obviously fake.
Continuity mistake: When Bond is beside the train going through the station there is nothing on the left, but as the train leaves a platform has appeared, and an engine shed and a brick bridge This was filmed back at the main station because of the double track set up.